Question: The following line passes through point $(-9, 1)$ : $y = -\dfrac{3}{13} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-9, 1)$ into the equation gives: $1 = -\dfrac{3}{13} \cdot -9 + b$ $1 = \dfrac{27}{13} + b$ $b = 1 - \dfrac{27}{13}$ $b = -\dfrac{14}{13}$ Plugging in $-\dfrac{14}{13}$ for $b$, we get $y = -\dfrac{3}{13} x - \dfrac{14}{13}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-9, 1)$